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I am running a multilevel logistic regression with a dichotomous outcome. The outcome variable measures protest participation. About 10 percent of the overall sample reports positive answers, which varies between 2 and 23 percent across the different clusters. Each cluster is around 1000 observations, with a sample of 266.000 respondents.

The model converges, but one of the reviewers suggested looking into rare event analysis as a robustness check. However, I am not sure what that implies in the multilevel logit framework. I might be completely off track, but my best guess was to set up a Poisson multilevel model.

Any concrete suggestions or literature references are welcome!

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    $\begingroup$ 10% is not particularly rare, plus you have quite a large sample size - you appear to have around 27,000 observations of the event, with around 27 clusters, so I do not understand why a reviewer would make this suggestion. If the outcome is binary, then a logistic model makes sense. A Poisson model does not, since the outcome is not a count. $\endgroup$
    – Robert Long
    Commented Jan 18, 2019 at 17:50
  • $\begingroup$ Hi! The question is still open, I have to answer something to the reviewer. In some of the clusters it does go down to 3/4 percent which corresponds to a bit more than 2000 observations. $\endgroup$
    – Erdne Htábrob
    Commented Feb 19, 2019 at 17:23

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Your outcome does not appear to be a rare event. You could explain this to the reviewer with the appropriate citations (ie King and Zeng, 2001 - "We study rare events data, binary dependent variables with dozens to thousands of times fewer ones").

However, you could also use the Stata implementation of the rare events logit estimator with Clarify in Stata or with Zelig in R. Stata (Clarify) will let you quickly estimate a rare events model with correlations in your clusters. The clustering option does not exist in R (Zelig), but you correct the standard errors to correct for the correlations. Regardless, I would bet your results will hold in this framework, even if it is not a multilevel model. You could tell the reviewer that this should not be in the paper since it isn't a rare event, but that the results are robust and include the aforementioned models.

As mentioned, the Poisson does not make sense your outcome is dichotomous and not a count.

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  • $\begingroup$ If you think this answer resolved your question, please go ahead and accept it. If not, please let me know why. $\endgroup$
    – BHudson
    Commented Feb 21, 2019 at 16:02
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    $\begingroup$ @eborbath said in comments above that "In some of the clusters it does go down to 3/4 percent which corresponds to a bit more than 2000 observations" - I agree, this is not the sort of sparsity that would cause convergence issues. This is an acceptable answer to the reviewer IMO. $\endgroup$
    – Weiwen Ng
    Commented Feb 27, 2019 at 15:35

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